The proposed SEP algorithm is an algorithm that uses the ZEST method at given locations but differs in the way the locations to be tested are selected. In particular, we make use of a pool of four locations that are being tested at any given point in time and which are initially selected as those with highest uncertainty according to their initial PMF. The algorithm then automatically and dynamically removes terminated locations from this pool and adds new locations in a way that reduces the overall uncertainty of the visual field as much as possible.
In practice, at each stimuli presentation, one of four locations in the pool is selected randomly and tested by using ZEST as described above. This is done until one of the four locations finishes, at which point it is removed from the pool. A new location is then added in the following way: (1) the current PMFs of all locations are placed into the visual field model; (2) the visual field model is then used to approximate the most likely PMF for each unfinished location as based on all responses over all locations; and (3) PMFs are then used to select the most informative location among the untested locations. To do this we define a function that is computed for each untested location and that combines two measures, namely, the Shannon entropy of the location estimate and its neighborhood heterogeneity,
\(\def\upalpha{\unicode[Times]{x3B1}}\)\(\def\upbeta{\unicode[Times]{x3B2}}\)\(\def\upgamma{\unicode[Times]{x3B3}}\)\(\def\updelta{\unicode[Times]{x3B4}}\)\(\def\upvarepsilon{\unicode[Times]{x3B5}}\)\(\def\upzeta{\unicode[Times]{x3B6}}\)\(\def\upeta{\unicode[Times]{x3B7}}\)\(\def\uptheta{\unicode[Times]{x3B8}}\)\(\def\upiota{\unicode[Times]{x3B9}}\)\(\def\upkappa{\unicode[Times]{x3BA}}\)\(\def\uplambda{\unicode[Times]{x3BB}}\)\(\def\upmu{\unicode[Times]{x3BC}}\)\(\def\upnu{\unicode[Times]{x3BD}}\)\(\def\upxi{\unicode[Times]{x3BE}}\)\(\def\upomicron{\unicode[Times]{x3BF}}\)\(\def\uppi{\unicode[Times]{x3C0}}\)\(\def\uprho{\unicode[Times]{x3C1}}\)\(\def\upsigma{\unicodeTimes]{x3C3}}\)\(\def\uptau{\unicode[Times]{x3C4}}\)\(\def\upupsilon{\unicode[Times]{x3C5}}\)\(\def\upphi{\unicode[Times]{x3C6}}\)\(\def\upchi{\unicode[Times]{x3C7}}\)\(\def\uppsy{\unicode[Times]{x3C8}}\)\(\def\upomega{\unicode[Times]{x3C9}}\)\(\def\bialpha{\boldsymbol{\alpha}}\)\(\def\bibeta{\boldsymbol{\beta}}\)\(\def\bigamma{\boldsymbol{\gamma}}\)\(\def\bidelta{\boldsymbol{\delta}}\)\(\def\bivarepsilon{\boldsymbol{\varepsilon}}\)\(\def\bizeta{\boldsymbol{\zeta}}\)\(\def\bieta{\boldsymbol{\eta}}\)\(\def\bitheta{\boldsymbol{\theta}}\)\(\def\biiota{\boldsymbol{\iota}}\)\(\def\bikappa{\boldsymbol{\kappa}}\)\(\def\bilambda{\boldsymbol{\lambda}}\)\(\def\bimu{\boldsymbol{\mu}}\)\(\def\binu{\boldsymbol{\nu}}\)\(\def\bixi{\boldsymbol{\xi}}\)\(\def\biomicron{\boldsymbol{\micron}}\)\(\def\bipi{\boldsymbol{\pi}}\)\(\def\birho{\boldsymbol{\rho}}\)\(\def\bisigma{\boldsymbol{\sigma}}\)\(\def\bitau{\boldsymbol{\tau}}\)\(\def\biupsilon{\boldsymbol{\upsilon}}\)\(\def\biphi{\boldsymbol{\phi}}\)\(\def\bichi{\boldsymbol{\chi}}\)\(\def\bipsy{\boldsymbol{\psy}}\)\(\def\biomega{\boldsymbol{\omega}}\)\begin{equation}\tag{1}{C_i} = {M_H}\left( i \right) + \alpha {M_G}\left( i \right),\end{equation}
where
MH (
i) and
MG(
i) are nonnegative and stand for the entropy and neighborhood heterogeneity of the visual field estimates at location
i, respectively. The parameter
α ∈ R
+ is a weight that influences the relative importance of these two factors. The next location is then selected as the one maximizing
Ci in
Equation 1, implying that either one or both of the defined measures should be high. The entropy measure,
MH (
i), quantifies the uncertainty of the modeled PMF of location
i, while the neighborhood heterogeneity,
MG(
i), represents an approximation of the spatial threshold gradient of the current field estimate (see
1 for computational details). In particular,
MG(
i) quantifies neighborhood threshold consistency and is higher at locations whose neighbor estimates differ from one another.
Note that
Equation 1 implicitly presumes that poor neighborhood consistency is a good indicator to test. Once the location with the highest
Ci is moved to the pool of locations to be tested, we substitute the PMF of the newly added location with that of the modeled PMF. This is achieved by summing the model PMF with a constant
δ, to reduce its confidence, and then multiplying it with the prior PMF. This effectively avoids being overconfident in the model probabilities.
With four locations in the pool again, the procedure restarts and continues until Ci is lower than a predefined value. In this case, no additional location is moved to the pool and the algorithm terminates as soon as the remaining three locations are finished. Importantly, this implies that SEP does not measure all visual field locations and infers sensitivity thresholds for the untested locations from the visual field model after termination of the algorithm.